I really hate this as a direction the industry is going: stream everything! That's fine for a lot of people who live in major metropolitan areas with lots of cell coverage. Here's the problem: we don't have reliable cellular service where we live. Yes, I have it in my house. But once I leave home to go to my wife's work place or down to town, half an hour to either place, no cell service. If I'm driving SE to Texas or Carlsbad, forget it. North to Ruidoso? Nada.
Apple is making their podcast app an increasing exercise in frustration with every iteration. If people want to stream, fine. I want to download apps and music and podcasts when I sync my phone in the morning, and that should be all there is to it. Everything that I've selected should be on the phone at that point, and NOTHING should say 'You have to turn on cellular service to play this podcast.' I DON'T CARE that there are other podcasts that I could stream, I have plenty to listen to and will download those others the next time I sync.
It's driven me to get books on Objective C and Swift and dust off the cobwebs on my C et al skills and roll my own podcast app. Yes, I occasionally look at various iTunes podcast apps in the store, haven't yet found one that did what I want. I'll gladly entertain suggestions for new apps.